Once you've played (and finished) a few games without founding a religion, you'll realize that it's not that essential to found one to win the game. Sure it's helpful, and games as Byzantium or Arabia lose out in civ-specific bonuses when they don't found, but even in these cases, it's not essential. And the realization that you don't need to found a religion to win helps one determine where Stonehenge belongs on the wonder-priority list, which is pretty close to the bottom. For me on deity, I either play a civ with a faith bonus, start near a faith mountain, start near multiple religious CS AND get lucky with easy quests, have a desert start AND get lucky enough to not get beaten to the pantheon, or just do without founding a religion.
Particularly on Deity level, where the safe option is to plan a path to victory without hard-building any pre-Renaissance wonders, or maybe 1 per era and beeline the tech as well as having pre-chops in place and a production switch ready. The only pre-medieval wonder that I attempt on deity is the Oracle because it's really the only early one that fulfills two very important considerations:
1.) It's one of the few wonders where a large portion of the payoff is only granted to the original builder. Top of my head, the only others are Great Library, LToP, Hagia Sophia, and Brandenburg. G-library is impossible on deity, LToP comes later so is more feasible, and with Brandenburg, if you're playing a game that needs generals, you're already going to have LOTS of them. Hagia Sophia might be something that some players shoot for, but I think the same rationale (above) why SH isn't worth the investment applies here as well.
2.) Accessibility - with some exceptions, notably the Maya AI, the AI usually doesn't prioritize Philosophy. They'll often get it after Civil Service. Contrarily, human players almost always aim for this tech as soon as building techs and minimal defensive techs are done because it unlocks NC. As such, this is probably the first tech that the human has before the deity AI gets.
As far as other early game wonder lists appearing on the thread, the one that I would add, very situationally, is Hanging Gardens. First, it's an SP-locked wonder, which increases the success rate. Second, I only try for it, and usually succeed, when you have a non-salt mining luxury start. Gold, silver, gems, and (hilltop) copper have great production yields but often can't be worked until later because you need other tiles to feed them. Often the capital has three of one type of luxury, so when it's one of these mining luxuries you need 6 food to feed them, conveniently what the wonder provides. Once I build it, I think of the three tiles as producing 2F/3P/2-4G each instead of the city having 6 extra food (even though this isn't entirely acccurate; tradition or ToA bonuses make it a little more than that) which helps to rationalize using these tiles which may slow growth but add economic stability and a great production boost.
Particularly on Deity level, where the safe option is to plan a path to victory without hard-building any pre-Renaissance wonders, or maybe 1 per era and beeline the tech as well as having pre-chops in place and a production switch ready. The only pre-medieval wonder that I attempt on deity is the Oracle because it's really the only early one that fulfills two very important considerations:
1.) It's one of the few wonders where a large portion of the payoff is only granted to the original builder. Top of my head, the only others are Great Library, LToP, Hagia Sophia, and Brandenburg. G-library is impossible on deity, LToP comes later so is more feasible, and with Brandenburg, if you're playing a game that needs generals, you're already going to have LOTS of them. Hagia Sophia might be something that some players shoot for, but I think the same rationale (above) why SH isn't worth the investment applies here as well.
2.) Accessibility - with some exceptions, notably the Maya AI, the AI usually doesn't prioritize Philosophy. They'll often get it after Civil Service. Contrarily, human players almost always aim for this tech as soon as building techs and minimal defensive techs are done because it unlocks NC. As such, this is probably the first tech that the human has before the deity AI gets.
As far as other early game wonder lists appearing on the thread, the one that I would add, very situationally, is Hanging Gardens. First, it's an SP-locked wonder, which increases the success rate. Second, I only try for it, and usually succeed, when you have a non-salt mining luxury start. Gold, silver, gems, and (hilltop) copper have great production yields but often can't be worked until later because you need other tiles to feed them. Often the capital has three of one type of luxury, so when it's one of these mining luxuries you need 6 food to feed them, conveniently what the wonder provides. Once I build it, I think of the three tiles as producing 2F/3P/2-4G each instead of the city having 6 extra food (even though this isn't entirely acccurate; tradition or ToA bonuses make it a little more than that) which helps to rationalize using these tiles which may slow growth but add economic stability and a great production boost.